Digital controllers are commonly designed for continuous-time systems. When the underlying system is significantly time varying, it is expected that so should be the controller. Often (as is the case with locally linearized models of nonlinear systems with fast changing operation regimes, or in adaptive implementations), long term values of the system parameters are not available. The purpose of the proposed research is to develop a design methodology that will address these issues: to look for a robust digital design that takes into account, indeed, that will optimize the continuous-time system behavior. That will be in contrast to most current designs which focus solely on the sample-time closed-loop evolution. The design methodology should be suitable for time-varying systems and require only (temporally) local numerical values of the system parameters. H-infinity, Graph and Gap control theory will provide the underlying paradigms. The immediate goals set forth in this proposal touch on issues at the focal point of current systems research, and are significant in realistic applications. The objectives will also give rise to several fundamental technical and conceptual questions: The closed-loop system evolves in hybrid-time (continuous and discrete). An appropriate framework for hybrid-time H-infinity analysis and optimization will have to be developed. The treatment of time-varying systems rules out direct use of transform domain techniques. This study is thus intended to follow and attempt to further extend the recent alternative path of a variational/game theoretical time domain approach to H-infinity design. It will also attempt to bridge the gap between this time domain approach and the standard operator theoretic/factorization based transform domain H-infinity analysis. Finally, reliance on temporally local models will require an adaptation the 1970's LQ "receding horizon" approach to the H-infinity framework, and the study of appropriate concepts of "slowly varying systems" that will give criteria to the success of "frozen time" based on receding horizon design.
